$p$-adic field search results

Results (displaying both matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
2.12.8.1	$12$	$x^{12} + 11 x^{9} + 3 x^{8} - 9 x^{6} - 90 x^{5} + 3 x^{4} - 27 x^{3} + 135 x^{2} + 27 x + 55$	$2$	$3$	$4$	$8$	$C_3 : C_4$ (as 12T5)	$4$	$3$	$[\ ]$	$[\ ]_{3}^{4}$	$t^{4} + t + 1$	$x^{3} + 2$	$[0]$	$[1]$
2.12.8.2	$12$	$x^{12} - 8 x^{3} + 16$	$2$	$3$	$4$	$8$	$C_3\times (C_3 : C_4)$ (as 12T19)	$12$	$3$	$[\ ]$	$[\ ]_{3}^{12}$	$t^{4} + t + 1$	$x^{3} + 2 t$	$[0]$	$[1]$